A class has three teachers, Mr. P, Ms. Q and Mrs.R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is k!(18), then the value of k is.
Open in App
Solution
Let T and S denotes teacher and student respectively. Then we have following possible patterns according to question (i) TSSTSSTSS (ii) STSSTSSTS (iii) SSTSSTSST Hence total number of arrangements are 3⋅(3!)6!=18×6!⇒k=6.